Well, theoretically it is dry clean only but really it is not. It mostly depends on the article of clothing itself and the manner of construction.
As for ink, inkjet ink will not be permanent(though I suppose you could dry clean it to give it a longer life). You would want to use a photocopy from a laser printer, preferably from a xerox machine rather than a home printer b/c you will have a higher probability of the right type of ink, though not gauranteed so test.
You would also need a solvent to aid in the transfer of the pic to the fabric, Jane Dunnewold recommends Dupont 3661s automotive lacquer thinner.
You can also screenprint on the chiffon. Though screenprinting inks will probably leave a "hand" on the fabric, though they could be thinned to lessen this. You can also screenprint using slightly thickened fiber reactive dyes. And I beleive(though not totally sure) you can thicken acid dyes too. With both these methods you would have to steam the item to set the dyes.
Re-reading your post you can thin the acryilic dyes and heat set them. You'll still have a slight "hand" to the fabric though. After heat setting you won't have to worry about the expense of dry cleaning
One thing to remember is that chiffon is a loose weave fabric so your image will be "light" so to speak b/c their is obviously less fabric for the dye/paints to adhere too.